tisdag 28 februari 2017

I have put up an update of realQM for inspection, with Chapter 6 presenting the basic model.
It includes in particular the following remark on the difference between realQM and the stdQM of text books:

Schrödinger approached mathematical modeling of the atom starting with wave functions and then seeking an equation satisfied by the wave functions as solutions, thus proceeding from solutions to equation rather than from equation to solutions as the normal approach with the equation formulated on physical principles.

This is reflected in the absence of any derivation of Schrödinger's equation from basic physical principles, which is a main defect of stdQM. Starting from solutions and then finding an equation satisfied by the solutions hides the physics, while starting with the equation requires physics to formulate the equation. And this is the essence of realQM!

fredag 24 februari 2017

Hundreds of scientists skeptical of climate change urged President Trump on Thursday to withdraw from the United Nations framework on global warming, arguing that doing so would support the administration's pro-jobs agenda and help "people bootstrap themselves out of poverty."

The letter asserts that carbon dioxide, considered by many scientists to be the primary cause of climate change, "is not a pollutant" at all, but a necessary ingredient for nourishing life on Earth.

The 300 scientists, led by well-known climate researcher Richard Lindzen of the Massaschusetts Institute of Technology, sent a letter to the White House with a petition urging the U.S. to exit from the U.N. Framework Convention on Climate Change.

Candidates Trump and Pence promised not only to keep the U.S. out of a harmful international climate agreement, but also to roll back misdirected, pointless government restrictions of CO2 emissions," the letter read. "Dr. Lindzen and hundreds of scientists support you in this.

Schrödinger interpreted quantum theory as a simple classical theory of waves. In his view, physical reality consists of waves and waves only.

He denied categorically the existence of discrete energy levels and quantum jumps, on the grounds that in wave mechanics the discrete eigenvalues are eigenfrequencies of waves rather than energies, an idea to which he had alluded at the end of his first Communication. In the paper "On Energy Exchange According to Wave Mechanics," which he published in 1927, he explained his view on this subject in great detail.

The quantum postulate, in Schrödinger's view, is thus fully accounted for in terms of a resonance phenomenon, analogous to acoustical beats or to the behavior of "sympathetic pendulums" (two pendulums of equal, or almost equal, proper frequencies, connected by a weak spring).

The interaction between two systems, in other words, is satisfactorily explained on the basis of purely wave-mechanical conceptions as if the quantum postulate were valid- just as the frequencies of spontaneous emission are deduced from the time-dependent perturbation theory of wave mechanics as if there existed discrete energy levels and as if Bohr's frequency postulate were valid.

The assumption of quantum jumps or energy levels, Schrödinger concluded, is therfore redundant: "to admit the quantum postulate in conjunction with the resonance phenomenon means to accept two explanations of the same process. This, however, is like offering two excuses: one is certainly false, usually both."

In fact, Schrodinger claimed, in the correct description of this phenomenon one should not apply the concept of energy at all but only that of frequency.

We contrast with the following account of Born's view of quantum mechanics as particle statistics:

Only four days after Schrödinger's concluding contribution had been sent to the editor of the Annalen der Physik the publishers of the Zeitschrift fur Physik received a paper, less than five pages long, titled On the Quantum Mechanics of Collision Processes, in which Max Born proposed, for the first time, a probabilistic interpretation of the wave function implying thereby that microphysics must be considered a probabilistic theory.

When Born was awarded the Nobel Prize in 1954 "for his fundamental work in quantum mechanics and especially for his statistical interpretation of the wave function," he explained the motives of his opposition to Schrödinger's interpretation as follows:

"On this point I could not follow him. This was connected with the fact that my Institute and that of James Franck were housed in the same building of the Göttingen University. Every experiment by Franck and his assistants on electron collisions (of the first and second kind) appeared to me as a new proof of the corpuscular nature of the electron."

Born's probabilistic interpretation, apart from being prompted by the corpuscular aspects in Franck's collision experiments, was also influenced, as Born himself admitted, by Einstein's conception of the relation between the field of electromagnetic waves and the light quanta.

In the just mentioned lecture delivered in 1955, three days before Einstein's death, Born declared explicitly that it was fundamentally Einstein's idea which he (Born) applied in 1926 to the interpretation of Schrödinger's wave function and which today, appropriately generalized., is made use of everywhere.

Born's probability interpretation of quantum mechanics thus owes its existence to Einstein, who later became one of its most eloquent opponents.

Weknow that the view of Born, when forcefully missioned by Bohr, eliminated Schrödinger from the scene of modern physics and today is the text book version of quantum mechanics named the Copenhagen Interpretation. We understand that Born objected to Schrödinger's wave mechanics because he was influenced by Einstein's 1905 idea of a "corpuscular nature" of light and certain experiments suggesting a "corpuscular nature" of electrons.

But associating a "corpuscular nature" to light and electrons meant a giant step back from the main advancement of 19th century physics in the form of Maxwell's theory of light as electromagnetic waves, a step back first taken by Einstein but then abandoned, as expressed by Jammer:

Born's original probabilistic interpretation proved a dismal failure if applied to the explanation of diffraction phenomena such as the diffraction of electrons.

In the double-slit experiment, for example, Born's original interpretation implied that the blackening on the recording screen behind the double-slit, with both slits open, should be the superposition of the two individual blackenings obtained with only one slip opened in turn.

The very experimental fact that there are regions in the diffraction pattern not blackened at all with both slits open, whereas the same regions exhibit strong blackening if only one slit is open, disproves Born's original version of his probabilistic interpretation.

Since this double-slit experiment can be carried out at such reduced radiation intensities that only one particle (electron, photon, etc.) passes the appara- tus at a time, it becomes clear, on mathematical analysis, that the $-wave associated with each particle interferes with itself and the mathematical interference is manifested by the physical distribution of the particles on the screen. The wave function must therefore be something physically real and not merely a representation of our knowledge, if it refers to particles in the classical sense.

Summing up:

Real wave mechanics in the spirit of Schrödinger makes a lot of sense, and that is the starting point of realQM.

Born's particle statistics does not make sense, and the big trouble is that this is the text book version of quantum mechanics.

How could it be, with these odds, that Born took the scene? The answer is the "obvious" generalisation of Schrödinger's wonderful 3d equation for the Hydrogen atom with one electron with physical meaning, into the 3N-dimensional linear Schrödinger equation for an atom with $N > 1$ electrons, a trivial generalisation without physical meaning. There should be another generalisation which stays physical and that is the aim of realQM.

In the end Schrödinger may be expected to take the game because he has a most perfect and efficient brain, according to Born.

To get more perspective let us quote from Born's 1954 Nobel Lecture:

Einstein, De Broglie, and Schrödinger have unceasingly stressed the unsatisfactory features of quantum mechanics and called for a return to the concepts of classical, Newtonian physics while proposing ways in which this could be done without contradicting experimental facts. Such weighty views cannot be ignored. Niels Bohr has gone to a great deal of trouble to refute the objections. I, too, have ruminated upon them and believe I can make some contribution to the clarification of the position.

Schrödinger thought that his wave theory made it possible to return to deterministic classical physics. He proposed (and he has recently emphasized his proposal anew’s), to dispense with the particle representation entirely, and instead of speaking of electrons as particles, to consider them as a continuous density distribution or electric density.

To us in Göttingen this interpretation seemed unacceptable in face of well established experimental facts. At that time it was already possible to count particles by means of scintillations or with a Geiger counter, and to photograph their tracks with the aid of a Wilson cloud chamber.

Born's argument against Schrödinger's wave mechanics in the spirit of Maxwell in favor of his own particle mechanics in the spirit of Newton, evidently was that a "tick" of Geiger counter or "track" in a cloud chamber both viewed to have "particle-like quality", can only be triggered by a "particle", but there is no such necessity...the snap of a whip is like a "particle" generated by a "wave"...

Born ends with:

How does it come about then, that great scientists such as Einstein, Schrö- dinger, and De Broglie are nevertheless dissatisfied with the situation?

Of course, all these objections are levelled not against the correctness of the formulae, but against their interpretation.

The lesson to be learned from what I have told of the origin of quantum mechanics is that probable refinements of mathematical methods will not suffice to produce a satisfactory theory, but that somewhere in our doctrine is hidden a concept, unjustified by experience, which we must eliminate to open up the road.

fredag 10 februari 2017

Erwin Schrödinger connects in Nature and the Greeks (1954) and in 2400 Jahre of Quantenmechanik (1948) the standard Copenhagen Interpretation of his wave function of quantum mechanics, back to the Greek atomists Leucippus and Democritus (born around 460 BC) preceded by the view of Anaximenes (died about 526) disciple of Anaximander of matter as collections of "particles" as "indivisible smallest bodies separated by void" subject to "rarefaction and condensation".

In the Copenhagen Interpretation wave functions are supposed to represent probability distributions of collections of electrons viewed as "particles in void" in the same way as the Greek atomists did 2500 years ago.

The contribution from modern physics to this ancient view is the element of probability eliminating causality by stating that "particles" are supposed to "jump around", or "jiggle" in the terminology of Feynman, without cause and thus always be nowhere and everywhere in the void at the same time.

Schrödinger compares this ancient "particle" view boosted by probability with his own opposite view that "all is waves without void obeying causality" as possibly a true advancement of physics. This is the starting point of realQM...as ontic/realistic/objective rather epistemic/idealistic/subjective...

Recall Roger Penrose in Foreword to Nature and the Greeks and Science and Humanism:

Moreover, in my personal view, the more "objective" philosophical standpoints of Schrõdinger and Einstein with respect to quantum mechanics, are immeasurably superior to "subjective" ones of Heisenberg and Bohr.

While it is often held that the remarkable successes of quantum physics have led us to doubt the very existence of an "objective reality" at the quantum level of molecules, atoms and their constituent particles, the extraordinary precision of the quantum formalism - which means, essentially, of the Schrõdinger equation - signals to us that there must indeed be a "reality" at the quantum level, albeit an unfamiliar one, in order that there can be a "something" so accurately described by that very formalism.

Over the past century, human activities have released large amounts of carbon dioxide and other greenhouse gases into the atmosphere.

Greenhouse gases act like a blanket around Earth, trapping energy in the atmosphere and causing it to warm. This phenomenon is called the greenhouse effect... and is natural and necessary to support life on Earth. However, the buildup of greenhouse gases can change Earth's climate and result in dangerous effects to human health and welfare and to ecosystems.

The reason that this propaganda is still on the EPA web page can only be that the new director of EPA Scott Pruitt has not yet been confirmed. It will be interesting to see the new web page after Pruitt has implemented the plan of Ebell to dismantle CO2 alarmism...in the US...and then...

In searching for an interpretation of quantum mechanics we seem to be faced with nothing but bad choices.

My own conclusion (not universally shared) is that today there is no interpretation of quantum mechanics that does not have serious flaws, and that we ought to take seriously the possibility of finding some more satisfactory other theory, to which quantum mechanics is merely a good approximation.

Weinberg's view is a theme on the educated physics blogosphere of today:

Sabine agrees with Weinberg that "there are serious problems", while Lubos insists that "there are no problems".

There are two approaches to mathematical modelling of the physical world:

Pick symbols to form a mathematical expression/equation and then try to give it a meaning.

Have a meaningful thought and then try to express it as a mathematical expression/equation.

Schrödinger's equation was formed more according to 1. rather than 2. and has resisted all efforts to be given a physical meaning. Interpreting Schrödinger's equation has shown to be like interpreting the Bible as authored by God rather than human minds.

What makes Schrödinger's equation so difficult to interpret in physical terms, is that it depends on $3N$ spatial variables for an atom with $N$ electrons, while an atom with all its electrons seems to share experience in a common 3-d space. Here is how Weinberg describes the generalisation from $N=1$ in 3 space dimensions to $N>1$ in $3N$ space dimensions as "obvious":

More than that, Schrödinger’s equation had an obvious generalisation to general systems.

Weinberg takes for granted that what "is obvious" does not have to be explained. But everything in rational physics needs rational argumentation and nothing "is obvious", and so this is where quantum mechanics branches off from rational physics. If what is claimed to be "obvious" in fact lacks rational argument, then it may simply be all wrong. The generalisation of Schrödinger's equation to $N>1$ fell into that trap, and that is the tragedy of modern physics.

There is nothing "obvious" in the sense of "frequently encountered" in the generalisation of Schrödinger's equation from 3 space dimensions to 3N space dimension, since it is a giant leap away from reality and as such utterly "non-obvious" and "never encountered" before.

In realQM I suggest a different form of Schrödinger's equation as a system in 3d with physical meaning.

The first postulate of quantum mechanics is that physical states can be represented as vectors in a sort of abstract space known as Hilbert space.

According to the second postulate of quantum mechanics, observable physical quantities like position, momentum, energy, etc., are represented as Hermitian operators on Hilbert space.

We see that these postulates are purely formal and devoid of physics. We see that the notion of Hilbert space and Hermitian operator are elevated to have a mystical divine quality, as if Hilbert and Hermite were gods like Zeus (physics of the sky) and Poseidon (physics of the sea)...much of the mystery of quantum mechanics comes from assigning meaning to such formalities without meaning...

The idea that the notion of Hilbert space is central to quantum mechanics was supported by an idea that Hilbert space as a key ingredient in the "modern mathematics" created by Hilbert 1926-32 should be the perfect tool for "modern physics", an idea explored in von Neumann's monumental Mathematical Foundations of Quantum Mechanics. Here the linearity of Schrödinger's equation is instrumental and its many dimensions doesn't matter, but it appears that von Neumann missed the physics:

I would like to make a confession which may seem immoral: I do not believe absolutely in Hilbert space no more. (von Neumann to Birkhoff 1935)

fredag 3 februari 2017

CO2 alarmism is based on an unphysical version of Stefan-Boltzmann's Law and associated Schwarzschild equations for radiative heat transfer stating a two-way radiative heat transfer from-warm-to-cold and from-cold-to-warm with net transfer as the difference between the two-way transfers.

This is expressed as "back radiation" from a colder atmosphere to warmer Earth surface in Kiehl-Trenberth's Global energy budget (above) and in Pierrehumbert's Infrafred radiation and planetary temperature based on Schwarzschild's equations, presented as the physical basis of CO2 alarmism.

In extended writing I have exposed the unphysical nature of radiative heat transfer from-cold-to-warm as violation of the 2nd law of thermodynamics, see e.g.

Massive two-way radiative heat transfer between two bodies is unphysical because it is unstable, with the net transfer arising from the difference between two gross quantities, and the 2nd law says that Nature cannot work that way: There is only transfer from-warm-to-cold and there can be no transfer from-cold-to-warm. Radiative heat transfer is always one-way from-warm-to-cold.

CO2 alarmism is thus based on a picture of massive radiative heat transfer back-and-forth between atmosphere and Earth surface (see above picture), as an unstable system threatening to go into "run-away-global-warming" at slightest perturbation. But there is no true physics behind this picture, only alarmist fiction.

Real physics indicates that global climate is stable rather than unstable, and as such insensitive to a very small change of the composition of the atmosphere upon doubling of CO2. There is little/no scientific evidence indicating that the effect could be measurable, that is be bigger than 0.5 C.

Note that climate models use Schwarzschild's equations to describe radiative heat transfer and the fact that these equations do not describe true physics is a death-blow to the current practice of climate simulation used to sell CO2 alarmism.

So, when you meet the argument that Pierrehumbert is an authority on infrared radiation and planetary temperature, you can say that this is not convincing because Pierrehumbert is using incorrect physics (which also comes out by the fact that he forgets gravitation as the true origin of the very high temperature on the surface of Venus and not radiation).

If now CO2 alarmism is based on incorrect physics or non-physics, then it may be fair to describe it as "hoax".

Think of it: Suppose that "scientific consensus" through MSM is bombarding you with a message that the Earth has to be evacuated because there is imminent fear that the "sky is going to fall down" because Newton's law of gravitation says that "everything is pulled down". Would you then say that "since it is said so it must be so" or would you say that this is a non-physical misinterpretation of Newton's law? Think of it!

The edX course Making Sense of Climate Science Denial is a typical example of the CO2 alarmism based on the incorrect physics of "back radiation", which is forcefully trumpeted by the educational system, as illustrated in the following key picture of the course: